scholarly journals Spatial externality and indeterminacy

2019 ◽  
Vol 14 (1) ◽  
pp. 102
Author(s):  
Emmanuelle Augeraud-Véron ◽  
Arnaud Ducrot
Keyword(s):  
Existence And Uniqueness ◽  
Supply And Demand ◽  
Uniqueness Of Solutions ◽  
Long Distance ◽  
Gaussian Kernels ◽  
Demand Curves ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Spatial Externality ◽  
The Impact

We study conditions for existence and uniqueness of solutions in some space-structured economic models with long-distance interactions between locations. The solution of these models satisfies non local equations, in which the interactions are modeled by convolution terms. Using properties of the spectrum location obtained by studying the characteristic equation, we derive conditions for the existence and uniqueness of the solution. This enables us to characterize the degree of indeterminacy of the system being considered. We apply our methodology to a theoretical one-sector growth model with increasing returns, which takes into account technological interdependencies among countries that are modeled by spatial externalities. When symmetric interaction kernels are considered, we prove that conditions for which indeterminacy occurs are the same as the ones needed when no interactions are taken into account. For Gaussian kernels, we study the impact of the standard deviation parameter on the degree of indeterminacy. We prove that when some asymmetric kernels are considered, indeterminacy can occur with classical assumptions on supply and demand curves.

scholarly journals Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1768
Author(s):  
Bin-Sheng Wang ◽  
Gang-Ling Hou ◽  
Bin Ge
Keyword(s):  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Uniqueness Of Solutions ◽  
Laplacian Equation ◽  
Uniqueness Of The Solution ◽  
Gradient Based ◽  
Surjectivity Result ◽  
Quasilinear Elliptic

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

scholarly journals A non-local macroscopic model for traffic flow

2021 ◽  
Author(s):  
Ioana Ciotir ◽  
Rim Fayad ◽  
Nicolas Forcadel ◽  
Antoine Tonnoir
Keyword(s):  
Traffic Flow ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Continuous Solution ◽  
Microscopic Model ◽  
Macroscopic Model ◽  
Estimate Error ◽  
Uniqueness Of The Solution ◽  
Non Local

In this work we propose a non-local Hamilton-Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.

scholarly journals Existence and Uniqueness of Solutions of the Semiclassical Einstein Equation in Cosmological Models

2021 ◽  
Author(s):  
Paolo Meda ◽  
Nicola Pinamonti ◽  
Daniel Siemssen
Keyword(s):  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Inversion Formula ◽  
Initial Conditions ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Expectation Values ◽  
Uniqueness Of Solutions ◽  
Stress Energy ◽  
Non Local

AbstractWe prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time, and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributions with derivative of the coefficient of the metric higher than the second are present in the expectation values of the stress-energy tensor and the term with the highest derivative appears in a non-local form. This fact forbids a direct analysis of the semiclassical equation, and in particular, standard recursive approaches to approximate the solution fail to converge. In this paper, we show that, after partial integration of the semiclassical Einstein equation in cosmology, the non-local highest derivative appears in the expectation values of the stress-energy tensor through the application of a linear unbounded operator which does not depend on the details of the chosen state. We prove that an inversion formula for this operator can be found, furthermore, the inverse happens to be more regular than the direct operator and it has the form of a retarded product, hence, causality is respected. The found inversion formula applied to the traced Einstein equation has thus the form of a fixed point equation. The proof of local existence and uniqueness of the solution of the semiclassical Einstein equation is then obtained applying the Banach fixed point theorem.

scholarly journals Existence results for Hadamard and Riemann-Liouville functional fractional neutral integrodifferential equations with finite delay

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4611-4618
Author(s):  
Mohamed Abbas
Keyword(s):  
Existence And Uniqueness ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Finite Delay ◽  
Uniqueness Of The Solution

By using Leray-Schauder?s alternative, we study the existence and uniqueness of solutions for some Hadamard and Riemann-Liouville fractional neutral functional integrodifferential equations with finite delay, whereas the uniqueness of the solution is established by Banach?s contraction principle. An illustrative example is also included.

scholarly journals Existence and Uniqueness of Solutions for the First Order Non-linear Differential Equations with Multi-point Boundary Conditions

2020 ◽  
Vol 13 (3) ◽  
pp. 414-426
Author(s):  
M.J. Mardanov ◽  
Y.A. Sharifov ◽  
Humbet Aliyev Aliyev ◽  
R.A. Sardarova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Non Linear ◽  
Uniqueness Of The Solution ◽  
Linear Differential ◽  
The Green Function

This article discusses the existence and uniqueness of solutions for the system of non-linear first order ordinary differential equations with multipoint boundary conditions. The Green function is constructed, and the problem is reduced to the equivalent integral equation. Existence and uniqueness of the solution to this problem is studied using the Banach contraction mapping principle and Schaefer’s fixed point theorem.

National freight demand modelling: a tool for macrologistics management

2018 ◽  
Vol 29 (4) ◽  
pp. 1171-1195 ◽  
Author(s):  
Jan Hendrik Havenga ◽  
Zane Paul Simpson
Keyword(s):  
International Trade ◽  
Supply And Demand ◽  
Developed Countries ◽  
Cost Models ◽  
Demand Model ◽  
Modal Shift ◽  
Long Distance ◽  
Content Type ◽  
Demand Modelling ◽  
The Impact

Purpose The purpose of this paper is to present the results of South Africa’s national freight demand model and related logistics cost models, and to illustrate the application of the modelling outputs to inform macrologistics policy. Design/methodology/approach Spatially and sectorally disaggregated supply and demand data are developed using the input-output (I-O) model of the economy as a platform, augmented by actual data. Supply and demand interaction is translated into freight flows via a gravity model. The logistics costs model is a bottom-up aggregation of logistics-related costs for these freight flows. Findings South Africa’s logistics costs are higher than in developed countries. Road freight volumes constitute 80 per cent of long-distance corridor freight, while road transport contributes more than 80 per cent to the country’s transport costs. These challenges raise concerns regarding the competitiveness of international trade, as well as the impact of transport externalities. The case studies highlight that domestic logistics costs are the biggest cost contributor to international trade logistics costs and can be reduced through inter alia modal shift. Modal shift can be induced through the internalisation of freight externality costs. Results show that externality cost internalisation can eradicate the societal cost of freight transport in South Africa without increasing macroeconomic freight costs. Research limitations/implications Systematic spatially disaggregated commodity-level data are limited. There is however a wealth of supply, demand and freight flow information collected by the public and private sector. Initiatives to create an appreciation of the intrinsic value of such information and to leverage data sources will improve freight demand modelling in emerging economies. Originality/value A spatially and sectorally disaggregated national freight demand model, and related logistics costs models, utilising actual and modelled data, balanced via the national I-O model, provides opportunities for increased accuracy of outputs and diverse application possibilities.

scholarly journals A non-local free boundary problem arising in a theory of financial bubbles

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130404 ◽  
Author(s):  
Henri Berestycki ◽  
Regis Monneau ◽  
José A. Scheinkman
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Obstacle Problem ◽  
Speculative Bubbles ◽  
Financial Bubbles ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
The Cost

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c , the cost of transacting the asset, goes to zero.

The methodological approach for the determination of the pressure of artificial raindrops as a question of the theory of splash soil erosion

2020 ◽  
pp. 24-28
Author(s):  
Mihail Zver'kov
Keyword(s):  
Block Diagram ◽  
Methodological Approach ◽  
Control Measures ◽  
Soil Conditions ◽  
Effective Pressure ◽  
Long Distance ◽  
Splash Erosion ◽  
Rain Drops ◽  
Artificial Rain ◽  
The Impact

To the article the results of the theoretical and experimental researches are given on questions of estimates of the dynamic rate effect of raindrop impact on soil. The aim of this work was to analyze the current methods to determine the rate of artificial rain pressure on the soil for the assessment of splash erosion. There are the developed author’s method for calculation the pressure of artificial rain on the soil and the assessment of splash erosion. The study aims to the justification of evaluation methods and the obtaining of quantitative characteristics, prevention and elimination of accelerated (anthropogenic) erosion, the creation and the realization of the required erosion control measures. The paper considers the question of determining the pressure of artificial rain on the soil. At the moment of raindrops impact, there is the tension in the soil, which is called vertical effective pressure. It is noted that the impact of rain drops in the soil there are stresses called vertical effective pressure. The equation for calculation of vertical effective pressure is proposed in this study using the known spectrum of raindrops. Effective pressure was 1.4 Pa for the artificial rain by sprinkler machine «Fregat» and 5.9 Pa for long distance sprinkler DD-30. The article deals with a block diagram of the sequence for determining the effective pressure of rain drops on the soil. This diagram was created by the author’s method of calculation of the effective pressure of rain drops on the soil. The need for an integrated approach to the description of the artificial rain impact on the soil is noted. Various parameters characterizing drop erosion are considered. There are data about the mass of splashed soil in the irrigation of various irrigation machinery and installations. For example, the rate (mass) of splashed soil was 0.28…0.78 t/ha under irrigation sprinkler apparatus RACO 4260–55/701C in the conditions of the Ryazan region. The method allows examining the environmental impact of sprinkler techniques for analyzes of the pressure, caused by raindrops, on the soil. It can also be useful in determining the irrigation rate before the runoff for different types of sprinkler equipment and soil conditions.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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